Find the Mass Moment of Inertia about the x,y,z axes

1. The problem statement, all variables and given/known data
The two small spheres of mass m each are connected by the light rigid rod which lies in the x-z plane. Determine the mass moments of inertia of the assembly about the x, y, z axes.

I have attached an image of the question

2. Relevant equations

3. The attempt at a solution

The answer is given but I don't understand how the answer is reached.

For Ixx The slender bar of length 2L has no mass moment of inertia about x. Then the other two rods each have a mass moment of inertia of 1/3*ml2 or do these cancel out and it's only the spheres which give the system a mass moment of inertia?

I think that, for the spheres, the mass moment of inertia should be:

2*(2/3)mr2 + 2ml2

Is the first portion, 2*(2/3)mr2, 0 because the radius is negligible small?

1. The problem statement, all variables and given/known data
The two small spheres of mass m each are connected by the light rigid rod which lies in the x-z plane. Determine the mass moments of inertia of the assembly about the x, y, z axes.

I have attached an image of the question

2. Relevant equations

3. The attempt at a solution

The answer is given but I don't understand how the answer is reached.

For Ixx The slender bar of length 2L has no mass moment of inertia about x. Then the other two rods each have a mass moment of inertia of 1/3*ml2 or do these cancel out and it's only the spheres which give the system a mass moment of inertia?

I think that, for the spheres, the mass moment of inertia should be:

2*(2/3)mr2 + 2ml2

Is the first portion, 2*(2/3)mr2, 0 because the radius is negligible small?

This would leave me with 2mL2

Any guidance would be appreciated. Thank you.

Anyone helping you will want a nice size image of that.

How far is each mass from each of the three possible axes of rotation?